High angular resolution polarimetric imaging of the nucleus of NGC 1068: Disentangling the polarising mechanisms
L. Grosset, D. Rouan, F. Marin, D. Gratadour, E. Lagadec, S. Hunziker, M. Montargès, Y. Magnard, M. Carle, J. Pragt, C. Petit
AAstronomy & Astrophysics manuscript no. Grosset2_corref_2 © ESO 2021February 15, 2021
High angular resolution polarimetric imagingof the nucleus of NGC 1068:
Disentangling the polarising mechanisms
L. Grosset , (cid:63) , D. Rouan , F. Marin , D. Gratadour , , E. Lagadec , S. Hunziker , M. Montargès , , Y. Magnard , M.Carle , J. Pragt , and C. Petit LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris Diderot,Sorbonne Paris Cité, 5 place Jules Janssen, 92190 Meudon, France SOFIA Science Center, USRA, NASA Ames Research Center, Mo ff ett Field, CA 94035, USA Université de Strasbourg, CNRS, Observatoire Astronomique de Strasbourg, UMR 7550, F-67000 Strasbourg, France Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304Nice cedex 4, France ETH Zurich, Institute for Particle Physics and Astrophysics,Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland Institute of Astronomy, KU Leuven, Celestijnenlaan 200D B2401, 3001 Leuven, Belgium Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France Aix Marseille Université, CNRS, CNES, LAM, Marseille, France NOVA Optical Infrared Instrumentation Group, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands DOTA, ONERA, Université Paris Saclay, F-91123, Palaiseau FranceReceived xx, 2020; accepted xx, 202x
ABSTRACT
Context.
Polarisation is a decisive method to study the inner region of active galactic nuclei (AGNs) since it is not a ff ected by contrastissues similarly to how classical imaging is. When coupled to high angular resolution (HAR), polarisation can help to disentangle thelocation of the various polarising mechanisms and then give an insight on the physics taking place on the core of AGNs. Aims.
We obtained a new data set of HAR polarimetric images of the archetypal Seyfert 2 nucleus of NGC 1068 observed withSPHERE / VLT and we aim in this paper at presenting the polarisation maps and at spatially separating the location of the polarisingmechanisms, thus deriving constraints on the organisation of the dust material in the inner region of this AGN.
Methods.
With four new narrow bands images between the visible and the near infrared combined to older broad band observations,we studied the wavelength dependency of the polarisation properties from 0.7 to 2.2 µ m of three selected regions within the inner2” surrounding the central engine. We then compared these measurements to radiative transfer simulations of scattering and dichroicabsorption processes, using the Monte-Carlo code MontAGN. Results.
We establish a detailed table of the relative importance of the polarising mechanism as a function of the aperture and of thewavelength. We are able to separate the dominant polarising mechanisms in the three regions of the ionisation cone, the extendedenvelop of the torus and the very central bright source of the AGN. Thus, we estimate the contribution of the di ff erent polarisationmechanisms to the observed polarisation flux in these regions. Dichroic absorption is estimated to be responsible for about 99 % ofthe polarised flux coming from the photo-centre. However, this contribution would be restricted to this location only, double scatteringprocess being the most important contributor to polarisation in the equatorial plane of the AGN and single scattering being dominantin the polar outflow bi-cone. Conclusions.
Despite that results are in good agreement with larger apertures measurements, the variety of situations with di ff erentmechanisms at play highlights the importance of spatial resolution for the interpretation of polarisation measurements. We also refinethe estimation of the integrated optical depth in the visible of the obscuring structure to a range of 20 to 100, constraining the geometryof the inner region of this AGN. Key words.
Galaxies: Seyfert, individual (NGC 1068), Techniques: polarimetric, high angular resolution, Methods: numerical,observational, Radiative transfer
1. Introduction
Thanks to the continuous progress of instrumentation, our un-derstanding of the organisation of the centre of active galacticnuclei (AGNs) has been growing fast in the last few years.In particular, we are now resolving at an unprecedented par-sec size spatial scale the core of nearby AGNs thanks to the de- (cid:63) e-mail: [email protected] velopment of high angular resolution (HAR) techniques, in par-ticular interferometry and extreme adaptive optics (AO), withthe help of polarisation. Recent ALMA observations of twoof the closest and brightest AGNs, NGC 1068 (García-Burilloet al. 2016, 2019; Imanishi et al. 2018, 2020; Lopez-Rodriguezet al. 2019; Impellizzeri et al. 2019) and Circinus (Izumi et al.2018), resolved at di ff erent frequencies the molecular mate-rial surrounding the central engine (CE), whose associated dust Article number, page 1 of 20 a r X i v : . [ a s t r o - ph . GA ] F e b & A proofs: manuscript no. Grosset2_corref_2 is thought to block the light emitted when observing the nu-cleus edge on, as proposed years ago by Antonucci & Miller(1985); Antonucci (1993). Using the GRAVITY interferometer(at VLTI), the Gravity Collaboration et al. (2018) was able toconstrain the shape of the broad line region of nearby quasar 3C273 to a rotating thick disk and identified the sublimation regionin NGC 1068 (Gravity Collaboration et al. 2020). Finally, thisview is completed thanks to the high contrast imaging coupledto polarimetry, as shown for instance by Packham et al. (1997,2007); Lopez-Rodriguez et al. (2015) with di ff erent instrumentsin the near to mid infrared range (Gratadour et al. 2015; Grossetet al. 2018).Indeed, polarimetric imaging is less a ff ected by contrast is-sues because polarisation provides more measurable intrinsicparameters of the light than just its intensity, namely the twoparameters describing the orientation of the linear polarisationand for some instruments the circular polarisation. Therefore,by looking at the polarisation of the incoming light, we can getaccess to information on the material responsible for the polar-isation, either by scattering, absorption or emission, even in thevicinity of bright sources. Polarisation has revealed itself to bevery e ffi cient to study media close to a very bright source typicalof AGNs environments, as demonstrated by Antonucci & Miller(1985), using polarised light to detect broad lines in the spectrumof NGC 1068.The model of the obscuring material surrounding the CE hasbeen undergoing evolutions, from simple torus shape in the early90’s (Antonucci 1993) to the current complex, clumpy and dy-namical environments such as those modelled by Izumi et al.(2018). Identifying the mechanism responsible for the polarisa-tion in AGNs brings information on the nature and characteris-tics of the scatterers. Several phenomena can be responsible forpolarisation, principally scattering on dust grains or on electrons(Antonucci & Miller 1985) or dichroic absorption or emission byelongated dust grains (Efstathiou et al. 1997; Lopez-Rodriguezet al. 2015).As concern the mechanisms giving rise to polarisation,single scattering is currently observed in the polarisation ofcircum-stellar environments, as for example by Kervella et al.(2015) with SPHERE / ZIMPOL (VLT, ESO’s Paranal observa-tory). More complex signatures have also been invoked in youngstellar objects, as the double scattering process presented byBastien & Menard (1990) and simulated by Murakawa (2010).This mechanism is also thought to be present in the outer en-velop of the obscuring material of AGNs (Grosset et al. 2018) toaccount for the observed polarisation in the 20 ×
60 pc centralregion (Gratadour et al. 2015).Dichroism is expected to induce polarisation closer to thevery central core of AGN. For elongated grains to emit or absorbphotons with a preferential polarisation orientation, it is requiredto have a mechanism responsible for aligning these grains on alarge enough scale (Efstathiou et al. 1997), typically on few par-secs size in the case of AGNs (Lopez-Rodriguez et al. 2015).Magnetic field has been a promising candidate for aligning dustgrains, and the measured polarisation could then be used to con-strain magnetic field properties, as achieved recently by Lopez-Rodriguez et al. (2015).There has been in the last years a growing number of simu-lation works to better understand the Physics of AGNs, throughpolarisation properties: Nenkova et al. (2002); Alonso-Herreroet al. (2011); Marin et al. (2015); Lopez-Rodriguez et al. (2015);Grosset et al. (2018) for example. The importance of polarisationin the understanding of AGNs is also revealed by the large quan-tity of polarimetric measurements on the AGN of NGC 1068, the archetypal Seyfert 2 galaxy (D ≈
14 Mpc), at all wavelengths onthe last 50 years, compiled by Marin (2018a).On this AGN, Antonucci & Miller (1985) first invoked scat-tering as the mechanism responsible for the polarisation, as itwould scatter above the equatorial plane toward the observerthe light emitted in the broad line region, hidden by the torus.Discussions about the nature of the scatterers, between electronsand dust grains, have been ongoing, Antonucci (1993) favouringelectrons due to the observed independence of the polarisationwith wavelength. Polarimetric observations by Packham et al.(1997) in the near infrared (NIR) confirmed the location of scat-terers in the polar region of NGC 1068 and it is now expectedthat both electrons and dust grains are populating this region.Packham et al. (2007) and Lopez-Rodriguez et al. (2016) indeeddetected polarisation in the narrow line region around 10 µ m,most likely produced by dichroic emission by dust, while Marinet al. (2015) combined both electrons and dust grains popula-tions in their simulations to study the polar outflows. Scatteringon dust grains has now been observed on NGC 1068 at mediumspatial scales (Gratadour et al. 2015, at about 100 to 200 pc).We obtained new polarimetric HAR images of NGC 1068thanks to SPHERE (installed at the Nasmyth focus of the UT3 -Melipal - of the VLT, at ESO’s Paranal observatory) in three nar-row bands (NB) in the NIR and one in the visible. In this paper,we present the data sets and discuss the evolution of the polar-isation in the di ff erent observed structures in the inner regionas a function of wavelength, in order to constrain the polarisingmechanisms. We detail in section 2 these new observations, andthe obtained polarimetric maps. We then present in section 3 thepolarisation as a function of wavelength in di ff erent selected re-gions of the AGN. In section 4, we detail how dichroism was in-troduced in the numerical simulations conducted using our codeMontAGN. We compare in section 5 the observations to the sim-ulations. We then discuss in section 6 this comparison and thenew insight brought by these new observations before conclud-ing.
2. Observations and data processing
This study is based on three data sets of the central region of theSeyfert 2 galaxy NGC 1068, obtained in polarimetric mode atHAR with the instrument SPHERE (Beuzit et al. 2008) at VLT,ESO Paranal Observatory.The first data are those of the SPHERE science verification(SV) observing program, obtained in H and Ks bands with thesub-module IRDIS (Dohlen et al. 2008; Langlois et al. 2014),published and analysed in Gratadour et al. (2015) and Grossetet al. (2018). The second set was observed between the 11 th and the 14 th of September 2016, also with the IRDIS system,bringing three additional NBs polarimetric images in the NIR,namely Continuum H, Continuum K1 and Continuum K2 (here-after Cnt H, Cnt K1 and Cnt K2 respectively). Filters propertiescan be found in Table 1. As for the first data set, the bright nu-cleus was used as a guide source for the SPHERE extreme adap-tive optics system SAXO (Fusco et al. 2006), giving a correctionquality comparable to what was achieved in the SV observation(SAXO could not be used at full capacity in both observationsdue to flux limitation). Seeing was comparable to previous run,ranging between 0.7 and 1.2” (a complete summary is availableon Table 1). Investigations on the radial profile of the centralpeak in all five NIR bands by Rouan et al. (2019) show no clear Article number, page 2 of 20. Grosset et al.: HAR polarisation in NGC 1068: location of polarising mechanisms modification of the PSF (see their figure 4) that could indicatechange in the resolution and the achieved angular resolution isestimated to 60 mas (i.e. 4 pc at 15 Mpc).NGC 1068 was also observed with ZIMPOL, anotherSPHERE sub-system (Schmid et al. 2018) in the 12 th of October2016, in the frame of the Other Science SPHERE guaranteedtime observation (GTO), adding the narrow band NR (NarrowRed, in the visible at 645.9 nm, see Table 1 for filter character-istics) to the available polarimetric data. Similarly to the IRDISobservations, SAXO was used but, due to the lack of photons,no information about the achieved angular resolution could beretrieved. SPARTA, the SPHERE system aimed at estimating theAO e ffi ciency is indeed known to su ff er bias in the case of fainttargets, and these informations are thus not reliable, as describedin Milli et al. (2017), highlighted in their figure 2. The seeingwas comparable to those of IRDIS and we can expect the AOcorrection to be similar, with lower achieved resolution due tothe wavelength-dependency on the AO correction. The achievedresolution can be estimated around 100–150 mas based on thesmallest structure detectable on the ZIMPOL image. A summaryof the observations is presented in Table 1.When observing in NIR, because of the sky emission becom-ing important, it is usual to match the sky observation integrationtime to the on-target integration time. However, because of thespecific data processing of dual polarimetric imaging, we do notneed sky acquisitions for each Half-Wave Plate (HWP) positionin polarimetric measurements, as displayed by Table 1. More de-tails about the polarimetric sky subtraction strategy will be de-veloped in an upcoming paper. ZIMPOL polarimetric maps (0.0036” per pixel, Schmid et al.2018) were created using the o ffi cial SPHERE-ZIMPOLpipeline. Maps of total and polarised intensities, degree of lin-ear polarisation and angle of linear polarisation are displayed inFigure 1.All IRDIS polarimetric images (from both observing runs)were reduced with the same dedicated pipeline including skysubtraction, flat field correction, realignment after a median fil-ter of size 3 × . The 8 final images were then realignedprecisely (IRDIS records two images with perpendicular polari-sation at the same time), before being combined using the inversematrix method , as described in Appendix A, to produce the in-tensity and polarisation Q and U maps. As detailed in Section 3.4and Appendix C, Cnt K2 (2266 nm) images were selected toavoid depolarisation due to SPHERE derotator.From these obtained maps, we finally transform them ontopolarised intensity I p lin , linear polarisation degree P lin and linearpolarisation position angle θ lin maps (Polarisation position anglereference follows I.A.U. (1973) recommendations, starting fromNorth and counting positive from North to East) following P lin = (cid:112) Q + U I , (1) I p lin = P lin × I (2) We also used double di ff erences and double ratios methods, with verysimilar outputs (see Tinbergen (1996) for more detail about these meth-ods). and θ lin =
12 atan2( U , Q ) (3)respectively.Maps were then corrected from distortion and true Northorientation. Images were shrinked along the vertical axis by afactor 1.006 and rotated using the orientation of the true Northas measured by Maire et al. 2016 of − . ◦ . Final NB maps,for IRDIS, with pixels of 0.01225” (more precisely evolving be-tween 0.012251” and 0.012265” per pixel, from H to Ks band,according to Maire et al. 2016) for the total and polarised inten-sities, the degree of linear polarisation, and the linear angle ofpolarisation are shown in Figures 2, 3 and 4.
3. Polarisation in selected areas
As can be seen in Figures 2, 3 and 4, the Cnt H (1573 nm) andCnt K1 (2091 nm) polarimetric maps harbour the same struc-tures as already identified by Gratadour et al. (2015) on broadH and Ks bands (1625 and 2182 nm respectively). Namely, weidentify a highly polarised (5 to 10 %) central source surroundedby a well defined polarised hourglass shaped region tracing thedouble ionisation cones and two low polarisation regions on theperpendicular direction to the hourglass axis at the level on thewaist (North-West and South-East), interpreted as a signatureof the obscuring material (Gratadour et al. 2015; Grosset et al.2018). The Cnt K2 (2266 nm) maps share some common pointswith the previous two wavelengths, the polarised central sourceis also present, although less polarised, and the low polarisationregion have a similar extension. However they also show somedi ff erences, the hourglass shaped structure being identified onthe polarised intensity map but harder to distinguish on the po-larisation degree and angle maps and the polarisation angle mapsshowing rather di ff erent behaviour. These peculiarities will bediscussed in Section 3.4.With a smaller field of view (FOV) of only 3 . (cid:48)(cid:48) × . (cid:48)(cid:48) , theZIMPOL NR (645.9 nm) image is to be compared with the cen-tral region of the NIR maps (FOV of 11 (cid:48)(cid:48) × . (cid:48)(cid:48) ). In the polari-sation degree map, we can recognise the elongated North-Southstructure seen in the inner 1” of the NIR maps, but no other struc-ture can be identified.To investigate the properties of the di ff erent identified struc-tures with respect to the wavelength, we extracted the global po-larimetric signal from several peculiar regions in the four NBsand the two broad bands (BB). We will focus on three impor-tant regions, the two south-western arcs laying between 1.5 and2.5” from the photo-centre, within the ionisation cone, the verycentral region at the photo-centre and the low polarisation dou-ble region surrounding the central source on the South-Est andNorth-West directions, between 0.5 and 1.5” from the centre. One major e ff ect to be taken into account when measuring po-larisation within aperture is the impact of the aperture’s size onthe measured polarisation. It is expected (see Table 2 of Lopez-Rodriguez et al. 2016 and Marin 2018a for polarisation depen-dency on the aperture size in NGC 1068) that the larger the aper-ture is the smaller the polarisation degree due to both increasingdilution by non polarised light and the inclusion of di ff erentlypolarised light within the aperture. This later e ff ect is especially Article number, page 3 of 20 & A proofs: manuscript no. Grosset2_corref_2
Table 1.
Log of the SPHERE observations (IRDIS and ZIMPOL)
Filter Date Obs time Sky time λ ∆ λ Seeing(UT) (min) (min) ( µ m) ( µ m) (”)(1) (2) (3) (4) (5) (6) (7)H 10-11 / / / / / / / / / / / / ≈ . Notes. (1) Filter name according to the SPHERE user manual. (2) Date of the observation (UT) (3) Observation integration duration, combiningall the HWP and dithering positions (4) Sky observation integration time, taken with one preferential HWP position (see text) (5) Filter centralwavelength (in µ m) (6) Filter full width at half maximum (in µ m) (7) Seeing (in arcseconds) as measured by the observatory, corrected for airmass.This is di ff erent from the achieved angular resolution, which is around 60 mas in the NIR and 100–150 mas in the red, as described in text. O ff s e t y ( a r c s e c ) Intensity N_R (log10(ADU)) O ff s e t y ( a r c s e c ) Polarised intensity N_R (log10(ADU)) O ff s e t y ( a r c s e c ) Degree of polarisation N_R (%) O ff s e t y ( a r c s e c ) Polarisation angle (deg)
Fig. 1.
Maps of intensity (in log (ADU / s), upper left panel), polarised intensity (in log (ADU / s), upper right panel), linear degree of polarisation(in %, bottom left panel) and linear angle of polarisation (in degrees, bottom right panel) in NR (645.9 nm) with ZIMPOL. North is up, and Eastis to the left. important here since we do see clear di ff erences at small scalebetween regions in the inner 2” of the AGN, in particular be-tween the very central region, the low polarisation region andthe South-western arcs. One major advantage of HAR in polaro-imaging is indeed to better resolve the polarised emission.As discussed in Tinbergen (1996), it is di ffi cult to evaluatethe quality of polarimetric maps. Signal to Noise Ratio (SNR)for example is not well defined since a higher intensity will notcorrespond to higher degree of polarisation. Furthermore, when the degree of polarisation is small, neither the polarisation anglenor the polarisation degree follow Gaussian distributions.We thus used two di ff erent methods, detailed in Appendix Bto evaluate the uncertainty on our polarisation measurements. Inour apertures, this uncertainty is generally ranging between 15and 20 % (see error bars of Figure 6 and Figure 9). Article number, page 4 of 20. Grosset et al.: HAR polarisation in NGC 1068: location of polarising mechanisms O ff s e t y ( a r c s e c ) Total Intensity (log10(ADU/s)) O ff s e t y ( a r c s e c ) Polarised Intensity (log10(ADU))
P = 5% 2.01.51.00.50.00.51.01.52.0
Offset x (arcsec)642 O ff s e t y ( a r c s e c ) Polarisation degree (%)
Offset x (arcsec)642 O ff s e t y ( a r c s e c ) Polarisation angle (degrees)
Fig. 2.
Maps of intensity (in log (ADU / s), upper left panel), polarised intensity (in log (ADU / s), upper right panel), linear degree of polarisation(in %, bottom left panel) and linear angle of polarisation (in degrees, bottom right panel) in Cnt H (1573 nm). Polarisation vectors have beenover-plotted to the Polarised intensity maps of upper right panel, with a length relative to the local polarisation degree. A reference length for a5 % vector is shown. North is up, and East is to the left. The two South-western arcs, identifiable around 2” South-Westof the central source, are detected in all the NIR polarisationmaps and directly on the intensity map of Cnt K1 and Cnt K2(2091 and 2266 nm respectively). We extracted the polarisationin 8 regions, of size 0 . (cid:48)(cid:48) × . (cid:48)(cid:48) , from East to West along eachof the arcs. A zoom on the two arcs and the apertures used hereare displayed in Figure 5. Aperture measurements are based onextraction of signal on the I, Q and U maps, translated onto finalpolarimetric parameters using eq. 1 and 3. Error bars are basedon the “pseudo-noise” approach of eq. B.1. The measured polar-isation degree and polarisation position angle for all filters aredisplayed in Figure 6.The first row of Figure 6 shows that the degree of linear po-larisation (displayed versus a position o ff set in this figure) in theSouth-western structures tends to increase as a function of wave-length in all apertures. This is illustrated in Figure 7, that repre-sents the evolution of the averaged degree of polarisation as afunction of wavelength in both arcs. We note that they evolve ona very similar linear increase, evidence for an unique mechanismbeing responsible for the polarisation in the two arcs. Further-more, the degree of polarisation, always higher in the outer arc, The size of the aperture was selected to be larger than any achievedresolution and to contain su ffi cient flux for significance, while keepingthe information as local as possible might suggest a scattering geometry configuration closer to 90 ◦ for this arc.The polarisation position angle, displayed in the second rowof Figure 6, is consistent with the expected variation for a centro-symmetric pattern, which is shown as the blue curve, computedas the orthogonal direction to the photo-centre for every apertureposition. Cnt K2 (2266 nm) is the most divergent from this pat-tern, and this case will be discussed in Section 3.4. We note how-ever that there is a trend, stronger for the outer South-westernarc, for the measured polarisation position angles to be o ff set byup to 20 ◦ , below the expected angles. Possible reasons for thiso ff set are multiples and are di ffi cult to disentangle. An o ff set be-tween the emission centre of the scattered light and the referencecentre of the image (the photo-centre in NIR) would produce ano ff set, but this o ff set should not depend on wavelength. A betterexplanation would be the addition of slightly di ff erent polarisa-tion orientation all along the extension of the arcs on the line ofsight (LOS). Inclination of these arcs with respect to the plane ofthe sky would also introduce an o ff set in the polarisation sincethe polarisation angle would not be 90 ◦ in this case. We analysed polarisation in the inner 2” of the AGN in dif-ferent apertures in order to properly interpret this complex re-
Article number, page 5 of 20 & A proofs: manuscript no. Grosset2_corref_2 O ff s e t y ( a r c s e c ) Total Intensity (log10(ADU/s)) O ff s e t y ( a r c s e c ) Polarised Intensity (log10(ADU))
P = 5% 2.01.51.00.50.00.51.01.52.0
Offset x (arcsec)642 O ff s e t y ( a r c s e c ) Polarisation degree (%)
Offset x (arcsec)642 O ff s e t y ( a r c s e c ) Polarisation angle (degrees)
Fig. 3.
Same as Fig. 2 for Cnt K1 (2091 nm). Red arrows indicate the position of the two South-western arcs. gion, where multiple polarisation mechanisms such as dichroicabsorption by aligned elongated grains, Thomson scattering onelectrons and Mie scattering on dust grains, may be in competi-tion.In particular, we analysed the very central 0.2” (hereafter“very centre”), encompassing the bright photo-centre, that showshigher polarisation degree than in its immediate surrounding andthat dominates the polarised flux. We also extracted polarisationfrom the very low polarisation regions surrounding this photo-centre, in the South-East and North-West directions, on the ex-pected extension of the obscuring material (hereafter “o ff cen-tre”). We finally considered a large aperture of 1” size (hereafterthe “central region”) in order to compare this study to other po-larimetric investigations references of this region at larger scale.These apertures are identified in Figure 8 and the measured po-larisation degree and polarisation position angle, as a function ofwavelength, are displayed in Figure 9.We also noted that, because the centre is very bright, thewings of the PSF of the central source could a ff ect the innermostmeasurements. Indeed, because this central source is polarised,part of the measured polarisation could be contaminated by thehigher polarisation from the centre, especially in the low polari-sation regions. The PSF in the K (2182 nm) band for SPHERE,contributes up to 10 % of the flux at ≈ ff centre” aper-ture, which ranges between ≈ ff ect significantly our measurements.Figure 9 reveals very di ff erent trends for the three apertures.The large aperture “central region” has an almost linearly in-creasing polarisation degree from 1.5 to 4 % between 0.7 µ m to2.2 µ m (left panel), while the “very centre” and the “o ff centre”regions evolve in a less monotonic way. As expected, the “o ff centre” aperture displays the lower polarisation degrees, < µ m to about 2-3 %. At the opposite, the“very centre” has a higher polarisation degree, starting at about2 % in R, increasing to a maximum of 5-7 % at ≈ . µ m andthen decreasing to ≈ µ m.As regards the polarisation position angle, it does not seem toundergo noticeable evolution, for all apertures and wavelengths.Measurements range between 90 and 130 degrees, encompass-ing the expected polarisation orientation in the central region inthe NIR of ≈ ◦ as measured by previous studies (Packhamet al. 2007; Gratadour et al. 2015). In most of the polarimetric maps and measurements in this work,Cnt K2 (2266 nm) results diverge from the other NIR ones. Inparticular, it exhibits a rather di ff erent behaviour compared tothe Cnt K1 and Ks filters, which are however at close wave-lengths (2091 and 2182 nm respectively). The Cnt K2 intensity Article number, page 6 of 20. Grosset et al.: HAR polarisation in NGC 1068: location of polarising mechanisms O ff s e t y ( a r c s e c ) Total Intensity (log10(ADU/s)) O ff s e t y ( a r c s e c ) Polarised Intensity (log10(ADU))
P = 5% 2.01.51.00.50.00.51.01.52.0
Offset x (arcsec)642 O ff s e t y ( a r c s e c ) Polarisation degree (%)
Offset x (arcsec)642 O ff s e t y ( a r c s e c ) Polarisation angle (degrees)
Fig. 4.
Same as Fig. 2 for Cnt K2 (2266 nm). Red arrows indicate the position of the two South-western arcs.
Fig. 5.
Position of the apertures along the two arcs, South-West fromthe central source, on top of a polarisation degree map in H (1.6 µ m). map features a narrower central peak, leading to a lower flux inthe surrounding of the very central peak. This limits the preci-sion of polarimetric measurements since non significant di ff er-ences between Q and U maps at low SNR are creating randompolarisation levels and explains at some extend these di ff erences.Indeed, these random polarisation levels outside the 1” inner re-gion pollutes the true polarised signal making its extraction moreuncertain. We also note that the polarisation in the most central region is slightly lower in this band, even on the area not a ff ectedby this problem. More problematic is the polarisation positionangle, which reveals very di ff erent patterns from other bands,within regions however shaped very similarly. Both the polarisa-tion position angle and degree are modified by a selection of theframes according to the SPHERE derotator position angle (seeAppendix C for more details), and we thus investigate the e ff ectof this on our polarimetric measurements in Appendix D.Since both the binned polarisation degree and polarised in-tensity maps of Figure D.1 reveal the features observed in theother NIR maps (especially the same polarisation degree of ≈
15 % in the South-western arcs), the di ff erence in intensityis likely to be the most impacting e ff ect on polarisation degreefor this NB. Using the selection for raw images only leads to alower SNR. Thus, our polarisation degree measurements shouldnot be contaminated at a significant level by systematics comingfrom derotator depolarisation issues. However, binning of polar-isation position angle map (Figure D.1) does not lead to an im-provement and an impact of the derotator position angle on themeasured angle is very likely there. We will thus not go furtherin our investigations for this polarisation position angle map.
4. Simulation of dichroism
Grosset et al. (2018) succeeded in reproducing using the ra-diative transfer code MontAGN the constant polarisation posi-tion angle and low polarisation degree over the central regionof NGC 1068 (about 20 ×
60 pc). This analysis was based on
Article number, page 7 of 20 & A proofs: manuscript no. Grosset2_corref_2
Fig. 6.
Degree (in %, first row) and angle (in degrees, second row) of polarisation as a function of position in the arc, from East to West, for theinner South-western arc (first column) and the outer South-western arc (second column), for all the observing bands (colour coded). Average valueof the polarisation degree in a given band is displayed by the respective colour horizontal lines. In plots of the second row, blue line correspondsto the expected polarisation position angle for these apertures if due to single scattering of light coming from the photo-centre of the AGN.
Fig. 7.
Degree of polarisation (in %), averaged for all 8 apertures in botharcs (colour coded) as a function of wavelength. a double scattering mechanism on spherical dust grains: pho-tons undergo two scattering events, one in the ionisation conewhere they are scattered back toward the equatorial plane wherethey are scattered a second time in the direction of the observer. These results are still in good agreement with the present paper’smeasurements. Especially, the overall polarisation position anglein the inner region and the low polarisation degree found in theSouth-East / North-West extension surrounding the very centre,are compatible with double scattering and is therefore strength-ening this interpretation. However, the relatively high ( ≈
15 %)polarisation degree of the photo-centre itself could not be ex-plained by these simulations.
Here we extend this simulation work through simulations of po-larimetric signal produced by dichroism. We used MontAGN(Grosset et al. 2018) to reproduce absorption of photons along astraight path through a region containing aligned elongated dustgrains. As we aim at reproducing a signal observed between 0.5and 2.3 µ m, we focused on dichroic absorption. Indeed, at thesewavelengths absorption is the dominant mechanism (Efstathiouet al. 1997) since temperature is expected to be high enough for asignificant dust emission below 2.3 µ m (ie. above ≈ ≤ ff er the dichroic absorption bythe rest of the colder dust structure surrounding it and will havelittle impact on the final polarisation, despite being possibly in- Article number, page 8 of 20. Grosset et al.: HAR polarisation in NGC 1068: location of polarising mechanisms
Fig. 8.
Position and size of the apertures used for polarimetric measure-ments, superimposed to the di ff erential polarisation angle map of BBH (1625 nm, from Gratadour et al. (2015)). The orange aperture corre-sponds to the “very centre”, the green to the “o ff -centre” and the red tothe “central region” as described in text. trinsically polarised. If this e ff ect is present, it would lower thedominant polarisation orientation flux, and thus slightly decreasethe dilution fraction required to match the observed polarisation(see Section 4.3 for more details about dilution).As MontAGN does not allow yet the user to align the dustgrains orientation along a preferential direction, it is impossibleto simulate dichroic absorption in the scattering framework ofGrosset et al. (2018). We thus focused on dichroism that we in-vestigated by simulating separately four polarisation orientationcomponents (Q + , U + , Q − and U − ). For each of them, we set thedust properties to match the dust population encountered by thisparticular polarisation orientation. We then combined the outputfiles to simulate the polarimetric properties of the resulting sig-nal, generated by dichroic absorption only. Following this method, we simulated polarimetric signals pro-duced by dichroic absorption for a range of optical depth( τ V ∈ [2 . , ff erent grain axis ratios. We useda ratio of major axis to minor axis of 1.5 (hereafter “r1:1.5”) anda ratio of 2 (hereafter “r1:2”). In both cases, we used a MRN(Mathis et al. 1977) size distribution with a power law of -3.5,ranging between 5 and 250 nm, with variation depending on theaxis ratios. Thus, for the first population, we used distributionranging between 5 and 125 nm for the minor axis and between7.5 and 188 nm for the major axis. For the “r1:2” population,we kept the same ratio for minor axis (between 5 and 125 nm)and set the major axis distribution between 10 and 250 nm. Weshow in this paper results for silicates dust grains, as simulations a factor of 2 in flux, unlikely large, would only lead to a lowering ofthe dilution fraction by up to ≈
5% because of the flux ratio of ≥
100 be-tween the two polarisation orientation observed in this simulation work. with graphites gave similar results. In a first step, photons pack-ets were emitted using a flat spectrum between 0.5 and 3 µ mand dust densities were set to match the chosen optical depth at0.5 µ m for each dust mixture integration.Because elongated grains preferentially absorb photons po-larised along their major axis, photons with di ff erent polarisa-tion orientations will not encounter the same optical depth alongtheir path through the same dust structure. For example, for our“r1:1.5” model we get values of τ V of 43.2, 6.8 and 25.0 alongthe Q + , Q − and U ± polarisation orientations respectively for anaveraged τ V = . ff erence of optical depth will translate into di ff erentfinal fluxes for each of the polarisation orientations, thus cre-ating a polarised signal. Simulated raw polarisation degree andpolarised intensity spectra are displayed in Figure 10.Polarisation is very important at short wavelengths as shownby right panel of Figure 10. Indeed, at short wavelengths,only one of the polarisation orientation propagates significantlythrough the dust structure because of its optical depth (lowfluxes, as shown by left panel), creating a 100 % polarised signal.At longer wavelength, the decrease of optical depth allow a frac-tion of the orthogonal polarisation to escape the obscuring ma-terial, and we thus observe a decrease in the polarised intensityand in the polarisation degree, especially for low optical depthmodels (where p ≈
0, right panel).
To compare our models with observations, we need to take intoaccount additional e ff ects. First, the flat spectrum used for emis-sion needs to be adapted to our AGN case and we multiplied theoutput flux, after normalisation, by a typical emission spectrum.We used a simple source SED (like Siebenmorgen et al. 2015for example) based on Rowan-Robinson (1995) approximationfor AGNs: λ F λ ∝ λ − . if λ < µ m; λ F λ ∝ λ − else . (4)Polarised intensity and polarisation Q corrected spectra areshown in Figure 11, for τ V in the range 2.5 - 200 and for thetwo grain axis ratios. The Q polarisation spectrum (right panel)is the main polarisation indicator since we aligned the grain axisalong the ± Q axis (Photons with a ± U polarisation orientationwill encounter a 50 /
50 grain axis ratio mixture), and indeed, val-ues of U do not exceed 0.0015 (0.15 % of the maximum of thedichroic flux). Absolute value of polarisation Q evolution showstwo phases. It first increases when the -Q photons, correspond-ing to the lowest optical depth, escape first and decrease when + Q photons become also able to escape. The polarised intensitygraph (left panel), translates the same trends when weighted bytotal intensity.In a second step, we need to properly account for dilutionby all other emission sources contributing to the flux measuredwithin the apertures. This is very critical since the high polarisa-tion degree values on the left panel of Figure 10 (at wavelength ≤ µ m) corresponds to very low fluxes (left panel) and willtherefore be reduced much more than the lower polarisation de-gree obtained at higher fluxes (at λ ≥ µ m).We used for dilution a library of spectra compiled by Marin(2018b). We used, similarly to them, the compiled spectrum of a we used a flat spectrum since we are more interested in transmissivityand since polarisation does not depend on the absolute intensity Q has negative values since here polarisation is produced horizon-tally with our model Article number, page 9 of 20 & A proofs: manuscript no. Grosset2_corref_2
Fig. 9.
Degree (in %, left panel) and angle (in degrees, right panel) of polarisation as a function of wavelength (in nm) for the three apertures in thecentral region of NGC 1068. “very centre” refers to the very inner 0.2”, “o ff -centre” to the region with an o ff set on the torus extension directionand “central region” to the large aperture integrating all the flux. See text of Section 3.3 for more detail about these apertures. Fig. 10.
Spectra of polarised intensity (first panel, with arbitrary intensity unit) and degree of polarisation (second panel) from dichroism simulatedwith MontAGN.
Fig. 11.
Spectra of relative polarised intensity (first panel) and normalised polarisation Q intensity (second panel) for an AGN emission fromMontAGN simulations. Polarised intensity is normalised to the maximum of the dichroic flux.Article number, page 10 of 20. Grosset et al.: HAR polarisation in NGC 1068: location of polarising mechanisms
Sbc galaxy (see their Figure 2), based on morphological classifi-cation of NGC 1068, such as Balick & Heckman 1985. A properspectrum, has then be added to the computed intensity spectra,after scaling by dilution fraction, computed at 1 µ m. Final SEDsand degree of polarisation are displayed in Figure 12 for dilutionfractions of 0.5 and 0.8.Right column of Figure 12 shows that dilution fraction andgrain axis ratio do have a similar influence on the polarisationdegree spectrum in mostly changing the amplitude but not theoverall shape of the curve. This implies that these two parametersare to some extent degenerated. We also note that the opticaldepth is the main parameter driving the shape of the curve andthus will be constrained by comparison with observations.
5. Comparison to observations
We computed fitting estimator maps as a function of opticaldepth and dilution fraction for both grain axis ratios. They wereobtained by computing the squared di ff erence between the ob-served and simulated – through dichroism – polarisation degreefor each data point, on the very central aperture . Maps are dis-played on Figure 13. Comparison of the observed data with thebest model curve for each grain axis ratio is shown in Figure 14. As shown by Figure 13, the dilution fraction is constrained to arather small range by the comparison between our observationand our simulations. Similarly, simulation also set a maximumand minimum limit values for the optical depth of the obscuringstructure.For the observed signal to be compatible with dichroic ab-sorption, a dilution fraction of 60 to 85 % is required, dependingslightly on the optical depth and the grain axis ratio. Thus, thefraction of the total intensity received in the very central sourceof NGC 1068 through dichroism, and therefore directly comingfrom the CE, would be of 15 to 40 % (at 1 µ m), in rather goodagreement with the ≈
5% polarisation observed at the very centrebetween 1.5 and 2.3 µ m.The integrated optical depth of the structure is also con-strained to values ranging between τ V ≈
20 to 100, slightlyfavouring values to the lower edge, with τ V ≤
50. Such dustdensities would allow enough light to propagate through the ob-scuring material in the NIR in one of the polarisation orientationto create the observed dichroic polarisation. This constraint doesnot depend on the geometry or on the clumpiness of the medium.Indeed, the obscuring material is very likely to be clumpy (seeeg. Marin et al. 2015), with individual clouds’ optical depth be-ing currently estimated to 45 ≤ τ V ≤
115 for example by Lopez-Rodriguez et al. (2015); Audibert et al. (2017). Thus, our con-straint would be compatible with an estimate of 1 to 2 clouds inour line of sight to the CE.
The other conclusion than can be driven from Figure 13 is thateven though the grain axis ratio does impact the optical depthdi ff erence between the two polarisation orientations, it does nottranslate into as large a di ff erence in the measured polarisationdegree. By comparing the two maps of Figure 13, the di ff erenceintroduced by a change in the grain axis ratio only slightly shiftboth the required dilution fraction and structure’s optical depthtoward larger values. For instance, we measured for our second Article number, page 11 of 20 & A proofs: manuscript no. Grosset2_corref_2
Fig. 12.
Spectra of relative intensity (first column) and degree of polarisation (second column) for an AGN with dilution fractions of 50 % (firstrow) and 80 % (second row) from MontAGN simulations. Intensity is normalised to the maximum of the dichroic flux as detailed in text.
Fig. 13.
Least squares maps (in log scale) for “r1:1.5” (left panel) and “r1:2” (right panel) for dilution fraction varying between 0 and 100 %(horizontal axis) and for optical depth τ V between 2.5 and 200 (vertical axis). grain population a shift of ≈
10 % in the dilution fraction and anincrease of ≈
10 in the lower limit of the required optical depthin V.We only tested here two grain ratio populations with our sim-ple model, with an orientation identical for all of the grains. It is expected (Efstathiou et al. 1997) that grains are not all perfectlyaligned along the magnetic field and are precessing along thepreferred orientation direction and that only a fraction of themare actually similarly orientated. Efstathiou et al. (1997) studiesthe impact of grain axis ratios and precession of the grains on the
Article number, page 12 of 20. Grosset et al.: HAR polarisation in NGC 1068: location of polarising mechanisms
Fig. 14.
Degree of polarisation (in %) as a function of wavelength (innm) for both simulations and observations. Measurements are the sameas on Figure 9 first panel and represent the “very centre” in orange,the “o ff -centre” region in green and the whole “central region” in red.Simulated spectra are shown in blue, continuous line for a grain ratio of1:1.5 and dashed line for a ratio of 1:2, with corresponding optical depthand dilution fraction parameters to best fit the “very-centre” (orange)data points. polarisation signal and concluded that the e ff ect was small andcomparable to a dilution of the signal, similarly to what can beseen in Figure 13. This is consistent since a misalignment of partof the grain population would be modelled by a slightly di ff erentshape of grain. These results correspond to an optical depth lower than theone estimated by Grosset et al. (2018), which were requiring τ V ≈ ff ect. However, this previ-ous estimate used the polarimetric signal in all the central region(of 2”) of NGC 1068, thus including the very central emission.A high optical depth was therefore necessary to reproduce thepolarimetric signal especially in this very central region, other-wise the unpolarised flux of the CE would mask the polarisation.However, if we consider that this central polarisation originatesfrom dichroic absorption instead, we can lower the required op-tical depth and still produce double scattering polarisation signalout of the very centre. We verified this assumption and Figure 15shows the polarimetric signal from scattering based on simula-tions developed in Grosset et al. (2018), for an optical depth of45 in V. Pattern on the cone and equatorial region of Figure 15are similar to those of the τ V =
170 map of Grosset et al. (2018)and di ff ers only on the central ≈ ff erent framework of only spher-ical dust grains, and only elongated dust grains respectively. Inorder to have a complete view of the mechanisms at the origin ofthe polarisation signal in the NIR, a full simulation frameworkwould be required, and would be a very important extension ofthis work. Our polarisation measurements within the largest aperture (thered data points of Figure 14) are in fair agreement with the liter-ature for similar or larger apertures. In particular, Figure 9 showsan increasing trends between 500 and 2000 nm that fits well within the compilation of polarimetric measurements in Figure 2of Marin (2018a). This tends to confirm that our small aperturemeasurements are reliable and that we are separating di ff erentpolarisation mechanisms on these two regions that become com-bined in larger apertures. In particular, we can distinguish at least3 regions with di ff erent polarisation mechanisms: the very in-ner central spot dominated by dichroic absorption; the equato-rial region of the “o ff -centre” region, ranging between few pcto ≈
60 pc dominated by double scattering; and the bi-cone re-gion between 60 and 200 pc in the polar directions dominated bysingle scattering.
6. Discussion
Thanks to recent polarimetric studies (Gratadour et al. 2015;Lopez-Rodriguez et al. 2015; Grosset et al. 2018; Marin 2018a,this work), we are proposing a global scheme of the polarisationmechanisms in AGNs and in particular in NGC 1068.On the photo-centre, beyond 1 µ m we would detect lightcoming directly from hot dust in the very inner region of thetorus, heated by the CE (Lopez-Rodriguez et al. 2015). Due tonon-spherical grains more or less aligned by magnetic field, onlyone polarisation orientation preferentially propagates, the otherbeing more absorbed, creating the observed polarisation in theNIR at the very centre. Dichroism is the most likely polarisingmechanism in this region since it is the one able to produce suchhigh polarisation degrees (up to 15 %) and a constant polari-sation orientation. Beyond 2 µ m, the optical depth become lowenough for both the polarisation orientation to propagate throughthe material, leading to the observed decrease in the polarisationdegree.On the equatorial region, along the extension of the obscur-ing material, we detect a low polarisation likely to be producedby double scattering (Grosset et al. 2018) on a region centredon the photo-centre and extending on both the equatorial di-rection to about 30 pc, with a 20 pc total thickness on the po-lar direction (Gratadour et al. 2015). This mechanism becomesnegligible at the photo-centre because polarised flux becomescompletely dominated by the e ff ect of dichroic absorption at thephoto-centre (the central PSF). The low polarisation signal isthus only detected at location o ff seted from the photo-centre.Finally, on the polar directions, we detect a signal well ex-plainable by single scattering, on material located in the doubleionisation cone between few parsecs to about 200 pc. The ori-gin of this scattering signal is possibly due to multiple species,depending on the location.In the innermost regions, the material responsible for thescattering (see maps of Figures 2, 3 and 4 until 0.5”), zoomed onFigure 16, is rather unclear. We observe an extension of the highpolarisation degree along the polar direction, in H (1625 nm)and Ks (2182 nm) bands as already stated by Gratadour et al.(2015), but also on Cnt H (1573 nm) and K1 (2091 nm) polari-sation maps. This feature is remarkably perpendicular to the COstructure detected on the central 10 pc with ALMA by García-Burillo et al. (2019), and could be due to electron scattering onthe first 10 pc of the bi-cone, as invoked by Antonucci (1993)and observed by Antonucci et al. (1994) with the Hubble SpaceTelescope in the ultra-violet. But hot dust is known to be presentin the polar outflow (Ramos Almeida & Ricci 2017 and refer-ences therein) and would also be a good candidate for scatteringthe light emitted by the CE. In both situations, it is expected thatlight emitted or scattered this close to the AGN centre would Article number, page 13 of 20 & A proofs: manuscript no. Grosset2_corref_2
20 10 0 10 20Offset x (pc)201001020 O ff s e t y ( p c ) Linear degree of polarisation (%) for an inclination of 90 deg O ff s e t y ( p c ) Polarisation angle (degree) for an inclination of 90 deg
Fig. 15.
Simulated map of polarisation degree (left) and polarisation position angle (right) computed by MontAGN for an integrated optical depthof τ V =
45 along the equatorial line of sight, with an inclination angle of 90 ◦ at 1.6 µ m (without dichroism and without dilution). then cross through parts of the obscuring material, so that polar-isation due to Thomson / Rayleigh / Mie scattering could be thencombined to dichroic absorption by this material. As both thesee ff ects in these regions are expected to produce polarisation witha similar position angle, it would be very di ffi cult to disentanglethe exact contribution of each of these mechanisms. As Thom-son scattering on electrons is wavelength-independent, the mainpolarising mechanism is also likely to change between visibleand IR close to the very centre, depending on the optical depthof the obscuring material. Fig. 16.
Zoom on the polar extension of the detected polarisation de-gree, close to the very centre, on the Cnt K1 map (2.1 µ m). Size of theimage is ≈ ×
2” and colour scale is the same as Figure 3.
At larger scale, dust grains are likely to be dominant. Com-parison with ALMA data reveals that the Southern arcs are verylikely due to scattering on dusty material, present in the ioni-sation cone and directly illuminated by the CE (García-Burilloet al. 2016, 2019).As discussed in Section 5.4, depending on the size of theaperture used to measure the polarisation signal, di ff erent pro-portion of these – at least – three mechanisms must be used, thus leading to the di ff erences between our measurements andthe large aperture ones. Based on these measurements at HAR, we can attempt to esti-mate the relative contribution of these three mechanisms to thepolarised intensity, as a function of their location.As shown by Figure 7, the degree of polarisation in the scat-tering region of the Southern arcs is increasing with wavelength.This variation is due both to evolution in the polarised inten-sity – slightly increasing between H and Cnt K2 (from 1625 to2266 nm)– and to the global intensity which is strongly decreas-ing at large distance from the centre with increasing wavelength(see upper panels of Figures 2, 3 and 4). This is mostly due tothe decrease of the stellar emission in the inner few arc-secondsbetween H and Ks (1625 and 2182 nm respectively), as detailedin Rouan et al. (2019). A deeper study of the relation betweenthe optical depth of the dust structures and the intensity and po-larised intensity produced by this structure combined with datafrom ALMA, would be a very interesting extension of this work.In the equatorial region, o ff set from the photo-centre, the de-gree of polarisation is low and slightly increases toward 2.2 µ m.This increase of the polarisation degree in Ks is most likely re-lated to a decrease of the intensity as detailed in previous para-graph, a stronger e ff ect than what is observed on the Southernarcs, the polarised intensity being quasi constant in the equato-rial region. This is consistent with the results of Grosset et al.(2018) on double scattering that found a relatively constant lowpolarisation degree on the equatorial region (except on the verycentre) regardless the optical depth of the structure, as long asit is optically thick (since we would detect the centrosymmetricsingle scattering pattern if it was optically thin).Combining these measurements, we estimated the contribu-tion of dichroic absorption (versus scattering) to the polarisedflux in the central region for di ff erent aperture sizes. Results aredetailed in Table 2.Thus according to Table 2, polarised intensity in the NIR,at the photo-centre, is expected to come at about 98 % ± Article number, page 14 of 20. Grosset et al.: HAR polarisation in NGC 1068: location of polarising mechanisms
Table 2.
Contribution of dichroism to the polarised flux in di ff erentapertures for a given band (in %) Aperture Filter namesize (in ”) NR Cnt H H Cnt K1 Ks Cnt K2Wvl (nm) 646 1573 1625 2091 2182 22660.2 - (1) (1)
54 58 55 74 631 - (1)
40 43 42 64 513 - (1)
26 30 31 53 38
Notes.
Polarisation uncertainties range between 0.5 and 1 % for all mea-surements except for NR and we thus took a conservative value for un-certainties of 1 %. (1) The central polarisation feature that is expectedto be due to dichroic absorption is weaker in NR band and estimationof di ff erent contributions is thus not reliable in this band (large incerti-tudes). with the wavelength, with polarised flux in Ks band being stilldominated by dichroism even on a 3” aperture. This ratio mightbe decreasing on the Cnt K2 band, around 2.3 µ m, as the fractionis lowered to 38 % ± As stated in Section 5, our study tends to lower the estimation ofthe required optical depth along the LOS to the CE of the AGNderived by Grosset et al. (2018). This lower values originatesfrom a lower need of blocking the light directly coming from thecentre, as polarisation is rather created by dichroic absorption(about 99 %) than by double scattering (less than 2 %) in theLOS. As discussed at the end of Grosset et al. (2018) and on Sec-tion 5 of the present work, dichroic absorption better reproducesthe degree of polarisation at this location. We can thus set an up-per value to the dust opacity at τ V = ≈
20 - 100 in τ V constrained by ourmodel is consistent with what is generally expected for the ob-scuring structure of AGN (as eg. Packham et al. 1997; Lopez-Rodriguez et al. 2015; Audibert et al. 2017; Rouan et al. 2019),lowering the previously estimation of Grosset et al. (2018).We only simulated here integrated absorption along the LOSto the CE, and there is therefore no assumption on the geometryor the nature (fragmentation) of the obscuring structure. In the ≈
60 pc region of constant polarisation, double scattering pro-cess should still be involved and thus a dust density decreasingwith the radius is still likely required to e ffi ciently scatter pho-tons (Grosset et al. 2018). Furthermore, this hypothesis is con-sistent with recent studies by Izumi et al. (2018), who developeda multiphase dynamic torus model, with lower densities in theouter regions of the torus (R >
10 pc), based on ALMA observa-tions of the Circinus galaxy.We also resolved an elongation along the polar axis with ahigh polarisation degree in most of the NIR maps, close to thevery centre, on a ≈
10 pc scale. As discussed in Section 6.1,this could be due to scattering on electrons in the first parsecsof the ionisation cone or on hot dust in the outflow. What is sur-prising about this elongation is that both the polarisation degreeand polarisation position angle are remarkably constant all along the structure, while the intensity undergo large variations (thusreflected in the polarised flux), and while di ff erent mechanismswould be involved. Would it be possible for two polarising ef-fects (dichroism at the photo-centre and scattering on the po-lar extension encompassing the photo-centre) be able to producesuch similar polarisation? It is likely that dichroism does alsoa ff ect light scattered (or emitted) in the polar ionisation cone ifclose enough to the equatorial plane, since light would then haveto cross through parts of the obscuring material. But where doesthe transition between this two e ff ect take place? Estimating theexact contribution of both phenomena to polarisation in this po-lar extension is thus di ffi cult and would be an interesting study. Our estimation of the 98 to 99 % contribution of the dichroicabsorption to the polarised flux observed in the NIR is consis-tent with the assumption of Lopez-Rodriguez et al. (2015), whoused a fraction of 100 % to study the magnetic field in the cen-tral region of NGC 1068. Our measured polarisation degree inKs (2182 nm) of 4.4 ± ± τ K ≈ .
24, based onPackham et al. (1997). Having very similar values, we wouldderive identical strength estimation for the magnetic field of 4 to139 mG, as estimated by Lopez-Rodriguez et al. (2015). Ourmeasurements also confirms that with HAR, the position an-gle for the polarisation orientation is very similar to those mea-sured with larger apertures (Lopez-Rodriguez et al. 2015) andtherefore reinforces the hypothesis of a toroidal geometry forthe magnetic field (parallel to the polarisation position angle fordichroic absorption).
7. Conclusion and prospectives
We presented in this paper new observations of the core of thearchetypal Seyfert 2 galaxy NGC 1068 in NB filters with theextreme adaptive optics instrument SPHERE. Our polarisationmeasurements within large apertures are in good agreement withthe literature and fits well the expected behaviour of the po-larisation with wavelength. However, by separating the signalin smaller apertures, thanks to HAR imaging, we were able totrace rather di ff erent behaviours of polarisation regarding wave-length, depending on the location in the AGN environment, trac-ing as many di ff erent polarising mechanisms. Thanks to thesepolarimetric measurements, combined to the previous polarisa-tion maps in H and Ks (1625 and 2182 nm respectively), weinvestigated the properties of three major regions within the cen-tral 200 pc of the AGN and their associated dominant polarisingmechanism: – the electrons and dust scattering in the ionisation cone, rang-ing between few tens of parsecs to ≈
200 pc. In particular,the South-western arcs detected in the broad NIR bands byGratadour et al. (2015) were re-observed and are compatiblewith single scattering, most likely on dust grains; – the dust double-scattering equatorial central region of theAGN (the first scattering would be in the polar region, andthe second in the equatorial region) corresponding to con-stant polarisation orientation and degree on a 60 pc ×
20 pcarea, encompassing the photo-centre and tracing the outer
Article number, page 15 of 20 & A proofs: manuscript no. Grosset2_corref_2 envelop of the obscuring material (similarly to Grosset et al.2018); – the dichroic absorption of the light coming directly from thephoto-centre of the AGN, from the CE.Furthermore, we identified a fourth region, at the transitionbetween the photo-centre and the ionisation cone up to ≈
10 pcin the polar direction, displaying similar polarisation propertiesto the photo-centre, with lower total intensity. We interpret thissignal as a possible transition between dichroic absorption at thevery centre to electron or dust scattering with increasing distanceto the centre.This study highlights the importance of the spatial resolutionto study polarimetry and especially on regions where several po-larising mechanisms are at work. We were able to disentanglethe di ff erent mechanisms specific to each region, thanks to thiscombination of polarimetry and HAR, and by comparison withthe numerical code MontAGN.Invoking dichroic absorption and scattering simulations, weconstrained the integrated optical depth of the dusty obscuringmaterial and the dilution fraction by other emission. Integratedoptical depth is constrained within a range of 20 to 100 in thevisible for the obscuring material. For the scope of this work, wemodelled both dichroism and scattering separately before com-bining the results. Combining these two e ff ects in the same simu-lation will soon be implemented in MontAGN, to simulate morecomplex environments where both electron / dust scattering anddichroic absorption can be acting on the same photons, like inthe very inner region of AGNs.This work also argue in favour of an extension of the po-larimetric investigations at HAR toward longer wavelengths andparticularly to the 3 to 10 µ m domain where a switch in thepolarisation position angle is expected due to a change in thedichroic absorption / emission at these wavelengths (Efstathiouet al. 1997). Acknowledgements.
Based on observations collected at the European SouthernObservatory under ESO programmes 60.A-9361(A) and 097.B-0840(A). The au-thors would like to acknowledge financial support from the “Programme Na-tional Hautes Energies” (PNHE) and from “Programme National de Cosmologieand Galaxies” (PNCG) funded by CNRS / INSU-IN2P3-INP, CEA, and CNES,France. Authors thank the anonymous referee for useful comments helping toimprove the clarity of the paper. The authors also thank E. Lopez-Rodriguez, T.Paumard and J. Milli for useful discussions that improved the manuscript. LGthanks N. T. Lam and P. Vermot for their contributions to the simulation code.This project has received funding from the European Union’s Horizon 2020 re-search and innovation program under the Marie Skłodowska-Curie Grant agree-ment No. 665501 with the research Foundation Flanders (FWO) ([PEGASUS] Marie Curie fellowship 12U2717N awarded to M.M.). This research has madeuse of the SIMBAD database, operated at CDS, Strasbourg, France. This re-search made use of Astropy, a community-developed core Python packagefor Astronomy (Astropy Collaboration et al. 2013, 2018) and Matplotlib, a 2Dgraphics package used for Python for application development, interactive script-ing, and publication-quality image generation across user interfaces and operat-ing systems (Hunter 2007). References
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Appendix A: Matrix inversion method
The matrix inversion method was inspired by polarisation stateanalysers methodologies, see Zallat & Heinrich (2007) for in-stance. Indeed, by observing with a polariser, we apply to theinitial Stokes parameters on the incoming light the followingtransformation matrix W to get the measured intensities: I meas = W × S , (A.1)with S = IQU (A.2)and I meas = I I ... I n . (A.3)W depends on the angles θ n of the polariser for each imagerecorded: W = cos ( θ ) cos( θ ) sin( θ )cos ( θ ) cos( θ ) sin( θ ) ... cos ( θ n ) cos( θ n ) sin( θ n ) . (A.4)Because W may not be a square matrix, it is not alwaysinvertible. In practice, it will never be the case (having onlythree polarimetric measurements / images is rare because of thesymmetry of measurements) and we apply the pseudo-inverse( W T W ). Therefore, by applying ( W T W ) − W T on both sides, wecan compute S directly: S = ( W T W ) − W T I meas . (A.5)In our case, we have eight measurements with the four fol-lowing positions of the polariser: I meas = Q + Q − U + U − Q + Q − U + U − . (A.6)We then get the W matrix as following W = − −
11 1 01 − − . (A.7) Appendix B: Polarisation uncertainty
We first verified the significance of the measured polarisationaccording to the received intensity. Using formula developed onSimmons & Stewart (1985) and Everett & Weisberg (2001), wederived maps of the ratio of the polarised intensity over the stan-dard deviation of the corresponding intensity
I p /σ I . Assumingthat photon noise is dominant in the NIR bands, the derived val-ues close to the photo-centre are high (above 30) and we get I p /σ γ ≈ − σ I > σ γ ), we estimate the true I p /σ I value to be about 3 to4. Thus, the lowering correction to be applied to the polarisationestimation, based on equation 11 of Everett & Weisberg (2001)is of ≈
5% of its value (thus about 0.5% in polarisation degree).The value of
I p /σ I is lower in the case of the NR band and ourmeasurements should therefore be considered as maximum val-ues for polarisation in this band.In order to evaluate the uncertainty due to polarisation vari-ation within the apertures and compare the methods, we alsomade an analysis of the local variations of the degree and an-gle of polarisation. As detailed in Clarke & Stewart (1986), wesubtracted to each pixel a mean of the four closest pixels, creat-ing a “pseudo-noise” map m σ and then look at the dispersion ofthese values on all the maps, as follows: σ pol = . × med (cid:18)(cid:12)(cid:12)(cid:12)(cid:12) √ . m σ − med (cid:16) √ . m σ (cid:17)(cid:12)(cid:12)(cid:12)(cid:12)(cid:19) (B.1)Thus we ensure to compare the variations in polarisation onregions where the SNR of the intensity maps is almost identical,which is required since the SNR will a ff ect the determination ofthe degree of polarisation.In our apertures, this variation is generally ranging between15 and 20 % (see error bars of Figure 6 and Figure 9) and thuslarger than the correction to be applied to the measured polari-sation of 5 % determined previously. We thus used in this studyas polarisation estimator the measured one, P TRUE ≈ P MES . Ashighlighted by Simmons & Stewart (1985), this estimator is notvery e ffi cient for low signal to noise ratio but is converging to-wards the other polarisation estimators at I p /σ I ≥
2, a valuewell within our error bars.
Appendix C: SPHERE Derotator
The derotator angle is an important parameter for polarimetricobservations with SPHERE. It a ff ects the polarisation measure-ments and should therefore be carefully planned or taken intoaccount. Figure C.1 shows the polarimetric e ffi ciency depend-ing on the broad filter and derotator angle, extracted from theSPHERE instrument User Manual. Contrary to broad filters, NBones have not been tested and their polarimetric e ffi ciency istherefore unknown. We expect their e ffi ciency to follow the gen-eral trends of the other filters, but we have no proper way toverify this, nor to constrain exactly what is the e ffi ciency for agiven angle. We placed our observations on a graph indicatingfor each of them the derotator angle (figure C.2).A decent fraction of our observations have been conductedwithin the − ◦ → ◦ range, i.e. on optimal position for BB fil-ters. However this is notably not the case for some images takenwith the Cnt K1 and Cnt K2 filters. Contrary to Cnt K1 whoseresults look very compatible to what was observe in BBs, Cnt K2maps, when creating without selection (First panel of Figs. C.3,C.4 and C.5), shows low polarimetric signal. It also exhibits not Article number, page 17 of 20 & A proofs: manuscript no. Grosset2_corref_2
Fig. C.1.
Measurements of the instrumental polarisation e ffi ciency (notaccounting the telescope) for four BB filters. For best use of the DPImode, one should avoid the pink zone where the e ffi ciency drops below90 ◦ ( > ◦ loss due to cross-talks). For that, one should make sure thederotator angle stays < ◦ or > ◦ . From SPHERE User Manual. realistic polarisation position angle (First panel of Figure C.5),as discussed in Section 3.4. We therefore investigated the pos-sible relation between this lack of signal and the derotator po-sition and thus compared the final maps computed with all rawimages, and those obtained with a selection of raw images withan optimised derotator position. All final images are shown inFigure C.3,C.4 and C.5 and reveal that selection does a ff ect sig-nificantly the measured polarisation as the South-western arcsdisplays very di ff erent polarisation (flux and degree).As revealed by Figs. C.3, C.4 and C.5, derotator position an-gle a ff ects the measured polarisation degree and position angle,but also when outside the 15 – 75 ◦ angle range, for Cnt K2. Mapscreated using data taken with angles > ◦ do show very low lev-els of polarisation. For this reason, we did selected the first 40 %of frames, within the 15-75 ◦ region, but with lower instrumentaldepolarisation for Cnt K2 data reduction (Fig. 4).We also conducted for the same reasons, despite having somehigher polarimetric signal, the same experiment on Cnt K1 filter.Selection processes do not displays such di ff erences between fi-nal products and we thus keep the complete set of data for thedata reduction for this NB. Appendix D: The case of Cnt K2
It is already known (see eg. the SPHERE user manual) that theSPHERE derotator position has an impact on the measured po-larisation, at least in the BBs. This has been studied and depictedin the SPHERE instrument documentation. However, investiga-tions by the SPHERE team have been conducted only on theBB filters, while the NB filters, including Cnt K2, have not beencharacterised yet. Therefore, we can not derive strong conclu-sions about the exact impact of the depolarisation on the imagesin the NB filters. As the NB measurements in Cnt H and Cnt K1filters are rather consistent with BB measurements, we are how-ever more confident in the derived parameters, while Cnt K2output should be considered carefully, especially the polarisa-tion position angle. An analysis of the derotator positions in ourdata sets is detailed in Appendix C, and shows a clear variationof the polarisation as a function of the derotator for Cnt K2 (noclear evidences were found for other bands). We thus selectedaccordingly to this study the image set that introduced the lowerpossible depolarisation.With this set, it is clear that polarised signal does exist inCnt K2 band as shown by the polarised intensity map of Fig- ure 4 (upper right and bottom left panels), harbouring the twoSouth-western arcs. In order to better display the polarimetricsignal in the maps in this NB, we display in Figure D.1 polari-metric maps using binned I, Q and U maps. The South-westernarcs are clearly identified on the polarisation degree map (bin-ning reduces the e ff ect of the noise onto the polarimetric signalby averaging the intensity of a group of pixels). However, thisbinning does not seem to improve significantly the polarisationposition angle map. Article number, page 18 of 20. Grosset et al.: HAR polarisation in NGC 1068: location of polarising mechanisms D e r o t a t o r a n g l e ( d e g ) Derotator angle for CntHposang : -55.7degposang : -10.7degposang : 34.3degposang : 79.3deg D e r o t a t o r a n g l e ( d e g ) Derotator angle for CntK1posang : -55.7degposang : -10.7degposang : 34.3degposang : 79.3deg D e r o t a t o r a n g l e ( d e g ) Derotator angle for CntK2posang : -55.7degposang : -10.7degposang : 34.3degposang : 79.3deg
Fig. C.2.
Derotator position for NB observations, CntH, CntK1 and CntK2. The red bands indicates the zones that one should avoid when usingBBs. O ff s e t y ( a r c s e c ) Polarisation degree (%) O ff s e t y ( a r c s e c ) Polarisation degree (%) O ff s e t y ( a r c s e c ) Polarisation degree (%)
Fig. C.3.
Binned maps of linear degree of polarisation (in %) in NGC 1068 with Cnt K2. These maps were created using all available raw imagesfor first panel; only the 60 % of the frames outside the 15-75 ◦ red zone of Fig. C.2 (last two series of points) for second panel; and only the firstseries of points (40 %), within the red zone for the third panel. Third panel corresponds to the binned version of maps displayed in Fig. 4. O ff s e t y ( a r c s e c ) Polarised Intensity (log10(ADU/s)) O ff s e t y ( a r c s e c ) Polarised Intensity (log10(ADU/s)) O ff s e t y ( a r c s e c ) Polarised Intensity (log10(ADU/s))
Fig. C.4.
Same as Fig. C.3 but for linearly polarised flux (in ADU / s). O ff s e t y ( a r c s e c ) Polarisation angle (degrees) O ff s e t y ( a r c s e c ) Polarisation angle (degrees) O ff s e t y ( a r c s e c ) Polarisation angle (degrees)
Fig. C.5.
Same as Fig. C.3 but for linear polarisation position angle (in degrees). Article number, page 19 of 20 & A proofs: manuscript no. Grosset2_corref_2 O ff s e t y ( a r c s e c ) Polarised Intensity (log10(ADU/s)) O ff s e t y ( a r c s e c ) Polarisation degree (%) O ff s e t y ( a r c s e c ) Polarisation angle (degrees)
Fig. D.1.
Binned 8 × (ADU //